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mathsnerd2
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Algebra 5
DecisionProblemsinGroupTheory(L24).... ....5
LieAlgebrasandRepresentationTheory(M24)... ...5
ModularRepresentationsofFiniteGroups(L24)... ...6
Calculusandalgebra(L24)...... ...8
Representationsof?nitegroupsofLietype(L24)... ....8
CommutativeAlgebra(M24)...... ...9
Non-commutativealgebras(L24)...... ...9
VonNeumannAlgebras(L24)...... ...10
Analysis 12
TopologicalGroups(L24)....... ...12
TopicsinIn?niteGroups(M16)..... ...12
AnalysisontheDiscreteHypercube(L24)— Non–Examinable ....13
IntroductiontoFunctionalAnalysis(M24)..... ...14
ComplexDi?erentialEquations(L24)...... ....15
Ellipticpartialdi?erentialequations(M24)... .....15
Combinatorics 17
Combinatorics(M16)....... ...17
CombinatorialProbability(L16)...... ....17
HypergraphGames(E8)— Non–Examinable ......18
ArithmeticCombinatorics(M16)...... ...18
GeometryandTopology 19
TheX-raytransformingeometryanddynamics(L24)... ...19
AlgebraicTopology(M24)....... ...20
Di?erentialGeometry(M24)...... ...20
SpectralGeometry(L24)........ ...21
AlgebraicGeometry(M24)....... ...22
ComplexManifolds(L24)........ ...22
AlgebraicGroups(M24)...... ...24
FibreBundles(L16)........ ...24
AlgebraicCycles(L24)...... ...25
Logic 26
CategoryTheory(M24)...... ...26
SetTheoryandLogic(L24)....... ...27
NumberTheory 29
EllipticCurves(L24)...... ...29
LocalFields(M16)....... ...29
ErgodicTheory(L24)....... ...30
TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24)....31
AlgebraicNumberTheory(M16)..... ...31
ModularFormsandAutomorphicForms(L24)... ...32
Non-abelianLubin-Tatetheory(M24)— Non–Examinable ......32
Probability 3
AdvancedProbability(M24)...... ...3
StochasticNetworks(L24)...... ...3
StochasticLoewnerEvolutions(L16)...... .....3
StochasticCalculusandApplications(L24).... ...3
ParticlePhysics,QuantumFieldsandStrings 46
QuantumFieldTheory(M24)...... ...46
SymmetryandParticlePhysics(M24)...... ...47
StatisticalFieldTheoryandApplications(M24)... ....48
AdvancedQuantumFieldTheory(L24)...... ...49
StringTheory(L24)........ ...49
SupersymmetryandExtraDimensions(L24)... ....50
StandardModel(L24)....... ...51
SolitonsandInstantons(E16)..... ...52
Supergravity(E16)........ ...53
3
QuantumInformationandQuantumFoundations 54
IntroductiontoQuantumComputation(M16)..... ....54
QuantumInformation,EntanglementandNonlocality(M16). .....55
PhilosophyofClassicalandQuantumMechanics(M12,L12).. ....55
MathematicalAspectsofQuantumInformationTheory(L24). .....56
QuantumControl(L16)...... ...57
RelativityandGravitation 59
Cosmology(M24)........ ...59
GeneralRelativity(M24)....... ...61
AdvancedCosmology(L16)....... ...62
ApplicationsofDi?erentialGeometrytoPhysics(L24)... ......63
BlackHoles(L24)....... ...64
QuantumCosmology(E16)........ ...65
IntroductionToTwistorTheory(E16)...... ...66
Astrophysics 67
AstrophysicalFluidDynamics(M24)...... ....67
StructureandEvolutionofStars(M24)..... ....68
AccretionDiscs(L16)...... ...68
Galaxies(L24)......... ...69
PhysicalCosmology(L24)....... ...70
StellarandPlanetaryMagneticFields(L24).... ...71
I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.
So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?
What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?
Please help me I am clueless.
I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).
Thank you for your help. :)
DecisionProblemsinGroupTheory(L24).... ....5
LieAlgebrasandRepresentationTheory(M24)... ...5
ModularRepresentationsofFiniteGroups(L24)... ...6
Calculusandalgebra(L24)...... ...8
Representationsof?nitegroupsofLietype(L24)... ....8
CommutativeAlgebra(M24)...... ...9
Non-commutativealgebras(L24)...... ...9
VonNeumannAlgebras(L24)...... ...10
Analysis 12
TopologicalGroups(L24)....... ...12
TopicsinIn?niteGroups(M16)..... ...12
AnalysisontheDiscreteHypercube(L24)— Non–Examinable ....13
IntroductiontoFunctionalAnalysis(M24)..... ...14
ComplexDi?erentialEquations(L24)...... ....15
Ellipticpartialdi?erentialequations(M24)... .....15
Combinatorics 17
Combinatorics(M16)....... ...17
CombinatorialProbability(L16)...... ....17
HypergraphGames(E8)— Non–Examinable ......18
ArithmeticCombinatorics(M16)...... ...18
GeometryandTopology 19
TheX-raytransformingeometryanddynamics(L24)... ...19
AlgebraicTopology(M24)....... ...20
Di?erentialGeometry(M24)...... ...20
SpectralGeometry(L24)........ ...21
AlgebraicGeometry(M24)....... ...22
ComplexManifolds(L24)........ ...22
AlgebraicGroups(M24)...... ...24
FibreBundles(L16)........ ...24
AlgebraicCycles(L24)...... ...25
Logic 26
CategoryTheory(M24)...... ...26
SetTheoryandLogic(L24)....... ...27
NumberTheory 29
EllipticCurves(L24)...... ...29
LocalFields(M16)....... ...29
ErgodicTheory(L24)....... ...30
TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24)....31
AlgebraicNumberTheory(M16)..... ...31
ModularFormsandAutomorphicForms(L24)... ...32
Non-abelianLubin-Tatetheory(M24)— Non–Examinable ......32
Probability 3
AdvancedProbability(M24)...... ...3
StochasticNetworks(L24)...... ...3
StochasticLoewnerEvolutions(L16)...... .....3
StochasticCalculusandApplications(L24).... ...3
ParticlePhysics,QuantumFieldsandStrings 46
QuantumFieldTheory(M24)...... ...46
SymmetryandParticlePhysics(M24)...... ...47
StatisticalFieldTheoryandApplications(M24)... ....48
AdvancedQuantumFieldTheory(L24)...... ...49
StringTheory(L24)........ ...49
SupersymmetryandExtraDimensions(L24)... ....50
StandardModel(L24)....... ...51
SolitonsandInstantons(E16)..... ...52
Supergravity(E16)........ ...53
3
QuantumInformationandQuantumFoundations 54
IntroductiontoQuantumComputation(M16)..... ....54
QuantumInformation,EntanglementandNonlocality(M16). .....55
PhilosophyofClassicalandQuantumMechanics(M12,L12).. ....55
MathematicalAspectsofQuantumInformationTheory(L24). .....56
QuantumControl(L16)...... ...57
RelativityandGravitation 59
Cosmology(M24)........ ...59
GeneralRelativity(M24)....... ...61
AdvancedCosmology(L16)....... ...62
ApplicationsofDi?erentialGeometrytoPhysics(L24)... ......63
BlackHoles(L24)....... ...64
QuantumCosmology(E16)........ ...65
IntroductionToTwistorTheory(E16)...... ...66
Astrophysics 67
AstrophysicalFluidDynamics(M24)...... ....67
StructureandEvolutionofStars(M24)..... ....68
AccretionDiscs(L16)...... ...68
Galaxies(L24)......... ...69
PhysicalCosmology(L24)....... ...70
StellarandPlanetaryMagneticFields(L24).... ...71
I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.
So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?
What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?
Please help me I am clueless.
I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).
Thank you for your help. :)